Combinatorics, automata and number theory

著者

• Berthé, V. (Valérie)
• Rigo, Michel

書誌事項

Combinatorics, automata and number theory

edited by Valérie Berthé, Michel Rigo

（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 135）

Cambridge University Press, 2010

• : hardback

注記

Includes bibliographical references (p. 563-593) and indexes

内容説明・目次

内容説明

This collaborative volume presents trends arising from the fruitful interaction between the themes of combinatorics on words, automata and formal language theory, and number theory. Presenting several important tools and concepts, the authors also reveal some of the exciting and important relationships that exist between these different fields. Topics include numeration systems, word complexity function, morphic words, Rauzy tilings and substitutive dynamical systems, Bratelli diagrams, frequencies and ergodicity, Diophantine approximation and transcendence, asymptotic properties of digital functions, decidability issues for D0L systems, matrix products and joint spectral radius. Topics are presented in a way that links them to the three main themes, but also extends them to dynamical systems and ergodic theory, fractals, tilings and spectral properties of matrices. Graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, fractals, tilings and stringology will find much of interest in this book.

目次

• Introduction Valerie Berthe and Michel Rigo
• 1. Preliminaries
• 2. Number representation and finite automata Ch. Frougny and J. Sakarovitch
• 3. Abstract numeration systems P. Lecomte and M. Rigo
• 4. Factor complexity J. Cassaigne and F. Nicolas
• 5. Substitutions, Rauzy fractals, and tilings V. Berthe, A. Siegel and J. Thuswaldner
• 6. Combinatorics on Bratelli diagrams and dynamical systems F. Durand
• 7. Infinite words with uniform frequencies, and invariant measures S. Ferenczi and T. Monteil
• 8. Transcendence and Diophantine approximation B. Adamczewski and Y. Bugeaud
• 9. Analysis of digital functions and applications M. Drmota and P. Grabner
• 10. The equality problem for purely substitutive words J. Honkala
• 11. Long products of matrices V. Blondel and R. Jungers
• References
• Notation index
• General index.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB02972048
• ISBN:
  • 9780521515979
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge, UK ; Tokyo
• ページ数/冊数: xix, 615 p.
• 大きさ: 25 cm
• 分類:
  • DC22 : 511.6
• 件名:
  • LCSH : Combinatorial analysis
  • LCSH : Number theory
  • LCSH : Machine theory
• 親書誌ID:
  • BA00064663